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A SEMINAR REPORT ON STONES
Report submitted to:
Department of CIVIL ENGINEERING, GURU RAMDAS KHALSA
INSTITUTE OF SCIENCE & TECHNOLOGY
Stones
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Acknowledgement
Apart from the efforts of me, the success of any seminar report depends largely on the
encouragement and guidelines of many others. Firstly my special thanks to Mrs. Satish Soni
Sir(Head of Department for Civil Engg.) I take this opportunity to express my gratitude to the
people who have been instrumental in the successful completion of this report.
I would like to show my greatest appreciation to Mrs. Garima Mishra (Asst. Prof.) I can’t say
thank you enough for his tremendous support and help. I feel motivated and encouraged every
time I attend his meeting. Without his encouragement and guidance this report would not have
materialized.
The guidance and support received from all the members who contributed and who are
contributing to this report, was vital for the success of the report. I am grateful for their
constant support and help.
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Contents
S.No. Topic discussed Pages(from– to)
1. Introduction to Stones/Rocks 4
2. India’s Glorious History 5
3. Geological Classification 5-9
4. Different types of Stones 9-16
5. Physical Properties of Stones 16-18
6. Conditions effecting disintegration 19-20
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Introduction
Stone is the one of the major building materials. It is a versatile material and hence it can be
used from the foundation to the parapet in a building and hence the scope comprises the study
of use of different stones at these places.
Introduction to Rocks
Rock (mineral), naturally occurring solid material consisting of one or more minerals.
Minerals are solid, naturally occurring chemical elements or compounds that are
homogenous, meaning they have a definite chemical composition and a very regular
arrangement of atoms. Rocks are everywhere, in the ground, forming mountains, and at
the bottom of the oceans. Earth’s outer layer, or crust, is made mostly of rock. Some
common rocks include granite and basalt.
Natural stone is used in building as a facing, veneer, and decoration. The major factors
affecting the suitability and use of stone fall under two broad, but overlapping
categories: physical and structural properties and aesthetic qualities. The three factors of
building stone that most influence their selection by architects for aesthetic reasons are
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8. References 22
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pattern, texture, and colour. Consideration also should be given to costs, availability,
weathering characteristics, physical properties, and size and thickness limitations.
Stone patterns are highly varied, and they provide special features that make building
stone a unique material. Texture is varied, ranging from coarse fragments to fine grains
and crystalline structures. Texture also varies with the hardness of minerals composing
the stone.
Pattern, texture, and colour all are affected by how the stone is fabricated and finished.
Granites tend to hold their colour and pattern, while limestone colour and pattern
changes with exposure. Textures may range from rough and flamed finishes to honed or
polished surfaces. The harder the stone, the better it takes and holds a polish.
India’s Glorious Tradition
India's long history, dating back to 3200 B.C. has been influenced considerably by the
disposition, development and use of stones and other construction materials. Dimension
stones have also left deep imprints on the architectural heritage of the country.
Innumerable temples, forts and palaces of Ancient Indian Civilization have been carved
out of locally available stones. The Taj Mahal at Agra stands testimony to the age
defying beauty of Indian marble. Some of the ancient rocks cut wonders are Khajuraho
Temple, Elephanta Caves, Konark Temple, etc. Besides, all major archaeological
excavations have revealed exquisitely carved statuettes and carvings in Stone. Ancient
Buddhist monuments like the Sanchi Stupa of 3rd century BC have also been carved out
of stone.
This tradition of Stone Architecture has continued to the present era with most of the
important modern buildings in India like the Presidential House, Parliament House and
Supreme Court made from high quality sandstone of Rajasthan. The Lotus Temple of
New Delhi stands testimony to the relevance of marble in modern Indian architecture.
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Stones are still the mainstays of civil construction in India, with stones being used
extensively in public buildings, hotels, temples etc. It is increasingly being used in
homes, with the use of stones now penetrating amongst the burgeoning middle class of
India.
GEOLOGICAL CLASSIFICATION OF ROCKS
1. Igneous Rocks
2. Sedimentary Rocks
3. Metamorphic Rocks
Igneous Rocks
Igneous rocks are rocks formed from a molten or partly molten material called magma.
Magma forms deep underground when rock that was once solid melts. Overlying rock
presses down on the magma, and the less dense magma rises through cracks in the
rock. As magma moves upward, it cools and solidifies. Magma that solidifies underground
usually cools slowly, allowing large crystals to form. Magma that reaches Earth’s surface is
called lava. Lava loses heat to the atmosphere or ocean very quickly and therefore
solidifies very rapidly, forming very small crystals or glass. When lava erupts at the
surface again and again, it can form mountains called volcanoes.
Igneous rocks commonly contain the minerals feldspar, quartz, mica, pyroxene,
amphibole, and olivine. Igneous rocks are named according to which minerals they contain.
Rocks rich in feldspar and quartz are called felsic; rocks rich in pyroxene, amphibole,
and olivine, which all contain magnesium and iron, are called mafic. Common and
important igneous rocks are granite, rhyolite, gabbro, and basalt. Granite and rhyolite are
felsic; gabbro and basalt are mafic. Granite has large crystals of quartz and feldspar. Rhyolite is
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the small-grained equivalent of granite. Gabbro has large crystals of pyroxene and olivine.
Basalt is the most common volcanic rock.
SedimentaryRocks
The most common types of clastic rocks are sandstone and shale (also known as
mudrock). Sandstone is made from sand, and shale is made from mud. Sand particles
have diameters in the range 2.0 to 0.06 mm (0.08 to 0.002 in), while mud particles are
smaller than 0.06 mm (0.002 in). Sand and mud form when physical or chemical
processes break down and destroy existing rocks. The sand and mud are carried by
wind, rivers, ocean currents, and glaciers, which deposit the sediment when the wind or
water slows down or where the glacier ends. Sand usually forms dunes in deserts, or
sandbars, riverbeds, beaches, and near-shore marine deposits. Mud particles are smaller
than sand particles, so they tend to stay in the wind or water longer and are deposited
only in very still environments, such as lake beds and the ocean floor.
Sedimentary rock forms when layers of sand and mud accumulate. As the sediment
accumulates, the weight of the layers of sediment presses down and compacts the
layers underneath. The sediments become cemented together into a hard rock when
minerals (most commonly quartz or calcite) precipitate, or harden, from water in the
spaces between grains of sediment, binding the grains together. Sediment is usually
deposited in layers, and compaction and cementation preserve these layers, called beds,
in the resulting sedimentary rock.
The most common types of chemical rocks are called evaporates because they form by
evaporation of seawater or lake water. The elements dissolved in the water crystallize
to form minerals such as gypsum and halite. Gypsum is used to manufacture plaster
and wallboard; halite is used as table salt.
The most common organic rock is limestone. Many marine animals, such as corals and
shellfish, have skeletons or shells made of calcium carbonate (CaCO3). When these
animals die, their skeletons sink to the seafloor and accumulate to form large beds of
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calcium carbonate. As more and more layers form, their weight compresses and
cements the layers at the bottom, forming limestone. Details of the skeletons and shells
are often preserved in the limestone as fossils.
Coal is another common organic rock. Coal comes from the carbon compounds of plants
growing in swampy environments. Plant material falling into the muck at the bottom of
the swamp is protected from decay. Burial and compaction of the accumulating plant
material can produce coal, an important fuel in many parts of the world. Coal deposits
frequently contain plant fossils.
Metamorphic Rocks
Metamorphic rock forms when pre-existing rock undergoes mineralogical and structural
changes resulting from high temperatures and pressures. These changes occur in the
rock while it remains solid (without melting).
The changes can occur while the rock is still solid because each mineral is stable only
over a specific range of temperature and pressure. If a mineral is heated or compressed
beyond its stability range, it breaks down and forms another mineral. For example,
quartz is stable at room temperature and at pressures up to 2 Gigapascals
(corresponding to the pressure found about 65 km [about 40 mi] underground). At
pressures above 2 Gigapascals, quartz breaks down and forms the mineral coesite, in
which the silicon and oxygen atoms are packed more closely together.
In the same way, combinations of minerals are stable over specific ranges of
temperature and pressure. At temperatures and pressures outside the specific ranges,
the minerals react to form different combinations of minerals. Such combinations of
minerals are called mineral assemblages.
In a metamorphic rock, one mineral assemblage changes to another when its atoms
move about in the solid state and recombine to form new minerals. This change from
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one mineral assemblage to another is called metamorphism. As temperature and
pressure increase, the rock gains energy, which fuels the chemical reactions that cause
metamorphism. As temperature and pressure decrease, the rock cools; often, it does
not have enough energy to change back to a low-temperature and low-pressure mineral
assemblage. In a sense, the rock is stuck in a state that is characteristic of its earlier
high-temperature and high-pressure environment. Thus, metamorphic rocks carry with
them information about the history of temperatures and pressures to which they were
subjected.
The size, shape, and distribution of mineral grains in a rock are called the texture of
the rock. Many metamorphic rocks are named for their main texture. Textures give important
clues as to how the rock formed. As the pressure and temperature that form a
metamorphic rock increase, the size of the mineral grains usually increases. When the
pressure is equal in all directions, mineral grains form in random orientations and point
in all directions. When the pressure is stronger in one direction than another, minerals
tend to align themselves in particular directions. In particular, thin plate-shaped
minerals, such as mica, align perpendicular to the direction of maximum pressure, giving
rise to a layering in the rock that is known as foliation. Compositional layering, or
bands of different minerals, can also occur and cause foliation. At low pressure,
foliation forms fine, thin layers, as in the rock slate. At medium pressure, foliation
becomes coarser, forming schist. At high pressure, foliation is very coarse, forming gneiss.
Commonly, the layering is folded in complex, wavy patterns from the pressure.
DIFFERENT TYPES OF STONES
Igneous Rocks
Granite -
Granite is an igneous rock, ordinarily composed of feldspar, mica, and silica or quartz. It
is formed by the cooling and crystallization of matter below the earth's surface under
conditions of heat and pressure which do not obtain in the case of lava ejected on the
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surface in a molten state. It is found in the eastern part of the United States, in
Canada, in many sections of the Rocky Mountains and as a rule, wherever the later rock
formations have been worn away by the weather, and the igneous rock has been
exposed.
Planes of Fracture -
The structure of granite is quite uniform, but there are often planes of cleavage caused
by stresses produced while the molten material was cooling. The plane along which the
rock can be split most easily is known as rift; it is often nearly horizontal. Rock can
also be split along a plane, known as the grain, which is perpendicular to the rift, but
this cleavage is not so easy as that along the rift. Sometimes, the stresses are sufficient
to cause fractures, called joints, running parallel to the surface.
Qualities of Granite -
Granite is one of the most valuable stones for construction purposes. Although the
quality of granite varies according to the proportions of the constituents and to their
method of aggregation, this kind of stone is generally durable, strong, and hard. The
hardest and most durable granites contain a greater proportion of quartz and a smaller
proportion of feldspar and mica. Feldspar makes granite more susceptible to
decomposition by the solution potash contained in it, potash feldspar being less durable
than lime or soda feldspar. Mica, being easily decomposed, is an element of weakness
in granite. An excess of lime or soda in the mica or feldspar hastens disintegration, as
does also an excess of iron. Therefore, stones showing large and dark iron stains should
be rejected for outside work. Fine-grained granite weathers better than does granite of
coarser grain.
Granite has a pearly lustre. The colour of common granite varies from white through
yellow to deep red, and the stone is generally classified as gray and red. Feldspar
renders the stone lighter in colour.
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Because of its uniform structure, granite can be quarried in large blocks. The rift, the
grain, and the joint planes are advantageous in quarrying, as it is very difficult to cut
granite in other places. The uses for which granite is suitable depend on the texture of
the stone. Medium-grained stone is best fitted for building construction. Fine-grained stone
can be carved and polished, but, on account of its extreme hardness, it cannot be
worked readily. Such stone is, therefore, costly when it has to be cut, Coarse-grained
granite should be used only for concrete aggregate.
TrapRocks -
The term trap is generally applied to a large variety of dark-coloured, igneous,
unstratified rock~ that occur in large tabular masses rising one above another in
successive steps like stairs. These rocks consist chiefly of hornblende, lime, feldspar, and
augite, with some magnetic and titanic iron. The predominance of one or the other of
these minerals gives rise to many distinctive names, as greenstone, olivine, etc. The
colour varies, being dark gray, dark green, or nearly black, according to the proportions
of the different constituents. The texture is usually so fine and close-grained that the
character of the structure cannot be determined by the naked eye.
Trap rocks are exceedingly dense, hard, and durable. However, they are not much used for
structural purposes because of their sombre and unattractive appearance, the great cost
of working, and the difficulty of securing large blocks on account of the numerous joint
planes. As they split and break easily, trap rocks are extensively used for paving blocks,
for the aggregate in making concrete, and for the construction of macadamized roads,
for which purpose their fine texture especially fits them. They are also used for railroad
ballast.
Sedimentary Rocks
Sandstone -
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Sandstone consists of fragments of other rocks cemented together. It is a stratified rock and
belongs to the later geological periods. Most of the grains are quartz, but often
feldspar is also present in sandstone. The cementing material may be silica, oxide of
iron, clay, or carbonate of lime.
If the cementing material is silica, the rock is very durable, but difficult to work. Iron
oxide is a good cementing material and gives the stone a reddish or brownish colour.
Clay is a satisfactory binder, but it readily absorbs water, which may cause destruction
of the stone by freezing. Lime renders the stone particularly liable to disintegration
when exposed to an atmosphere containing gases, or when used for foundations in a
soil that contains acid.
Sandstones -
Are variable in character, some being nearly as valuable as granite and others being
practically useless for permanent construction. The best stone is characterized by small
grains with a small proportion of cementing material. When broken, it has a bright, clear,
sharp fracture. It is usually found in thick beds and shows slight evidences of
stratification.
When quarried, sandstones are usually saturated with quarry water and are very soft;
but on exposure to the air, they dry out and become hard. Water can readily penetrate
between the layers of this stone; therefore, in foundations it should be laid on its
natural bed, that is, in the same position that it occupied in the quarry, so that the
penetration of moisture and possible disintegration by freezing may be prevented as
much as possible.
The colours of sandstone are white, cream, yellow, dark brown, blue, and red. Fine-
grained blue sandstone is known as bluestone. This variety is widely used for trimmings
and for stone sidewalks, as it readily splits into slabs.
Limestone -
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All limestones are of sedimentary origin and have for their principal ingredient
carbonate of lime. The presence of other minerals gives rise to the division of the
limestones into five classes, each of which is designated by the name of the
predominating mineral. When clay is present, the stone is called argillaceous limestone;
when silica predominates, siliceous limestone; when iron is prevalent, ferruginous
limestone; when magnesia is present to the extent of 15 per cent, magnesium
limestone; and when the carbonate of lime and the carbonate of magnesia are
combined in equal proportions, dolomite limestone. Limestones are either granular or
compact.
Granular limestone -
Consists of grains of carbonate of lime, cemented together by some compound of lime,
silica, and alumina. The grains are generally sea shells or fragments of shells and are
often mixed with sand. This kind of stone is always porous. It is found in various colours,
especially white and yellowish brown. In many cases, it is so soft when first quarried
that it can be cut with a knife; it hardens, however, on exposure to the air.
The variety of granular limestone called oolitic limestone is composed of egg-shaped
grains cemented together. It is one of the most important of the limestone group and
is extensively quarried and widely used for building purposes. Each grain is usually of
concentric structure, the carbonate of lime enclosing a particle of sand or of some
substance of either animal or vegetable origin.
Compact limestone -
Consists of carbonate of lime, either pure or mixed with sand or clay. This kind of
limestone is generally devoid of crystalline structure, and has a dull, earthy appearance
and a dark-blue, gray, black, or mottled colour. In some cases, however, it is crystalline
and full of organic remains; it is then known as crystalline limestone.
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The compact limestones are easily worked with the saw and hammer. They resemble
light granite in appearance, and are extensively used for building purposes. The variety
called shelly limestone, which consists of fossil shells that are cemented together, is
sufficiently hard to take a polish; it is much used for interior ornamentation. The
condition of the minerals combined with the lime also furnishes a basis for
distinguishing names. Thus, the stone is called hornstone when very fine grained silica is
present; cherty limestone, when the silica is in the form of rounded masses or nodules;
ironstone, when the amount of iron and clay is greater than the amount of lime;
rottenstone, when the ironstone is decomposed; and hydraulic limestone, when the rock
contains silica and clay in nearly equal proportions.
Shale -
Shale is a typical clay rock that splits readily in lines parallel to the bedding. Sand and
lime carbonate are always present in this stone and, with increase of either, the rock
grades into shaly sandstone or shaly limestone. Shale is used for light traffic roads and
in the manufacture of brick, tile, and other burned clay products, but it is not suitable
for concrete aggregate.
Conglomerate -
Stratified rock composed of rounded pebbles of any material, such as limestone, quartz,
shale, granite grains, feldspar, etc., cemented together is known as conglomerate. When
the pebbles are quartz with siliceous binding the rock is strong and hard to quarry or
dress. When the interstices between the pebbles are not filled by the binder, the rock
is very porous, and may hold great amounts of ground water. This stone is seldom used in
building construction.
Metamorphic Rocks
Marble -
Metamorphosed limestone gives the masonry material known as marble. It is easily dressed
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to a smooth surface and polished, and is considered one of the most valuable building
materials. It resists frost and moisture well, but like all limestones it does not withstand
fire.
Marble can be obtained in many colours, some of which are white, gray, red, blue,
green, and black. One of the most important characteristics of marble is that it is easy
to carve; the finer the grains of the stone, the more suitable it is for this purpose. The
fine white-grained varieties that are especially prized for sculpture are called saccharoid
marbles.
Some of the finest varieties of white American marble are found at Lee, Massachusetts,
and in the vicinity of Rutland, Vermont. The dark-blue marble from the Vermont
quarries is very durable and has a close grain. A fine black marble is quarried at Glens
Falls, New York. Coloured marbles, including gray, light and dark pink, buff, chocolate,
etc., are found in Tennessee, Georgia, and other states.
Slate -
Slate is a laminated rock of great hardness and density. It splits readily along planes called
planes of slaty cleavage. This facility of cleavage is one of the most valuable
characteristics of slate, as masses can be split into slabs and plates of small thickness
and great area.
The most common colours of slat are dark blue, bluish black, purplish gray, bluish gray,
and green; occasionally, red and cream-colored slates are also found. Some slates are
marked with bands or patches whose colour is different from that of the rest of the
stone. These marks do not affect the durability of the slate, but they spoil its
appearance.
Although slate is not strictly a building stone, it is used extensively for covering steps
and the roofs of buildings, for wall linings, and for sanitary purposes. Slate is sometimes
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used to make light traffic macadam, but, although it packs well, it ultimately yields
much mud and dust, which are objectionable.
Schist -
Schist has a more crystalline structure than slate, and the crystals are easily seen. It is
composed chiefly of minerals that cleave readily, such as hornblende, mica, etc., mixed
with a variable amount of granular quartz and feldspar. The presence of the cleavage
minerals produces a fine cleavage or foliation, called schistosity.
Schist is sometimes used in building construction but it disintegrates very rapidly and is
not durable. It should always be set with the planes of schistosity horizontal.
Gneiss -
Gneiss is a coarse-grained, laminated rock, formed by metamorphism of either
sedimentary or igneous rock. It is often used as structural material and as concrete
aggregate.
PHYSICAL PROPERTIES OF STONE
The physical characteristics of a particular stone must be suitable for its intended use.
It is important to determine the physical properties of the actual stone being used
rather than using values from a generic table, which can be very misleading.
Considerations of the physical properties of the stone being selected include modulus of
rupture, shear strength, coefficient of expansion, permanent irreversible growth and
change in shape, creep deflection, compressive strength, modulus of elasticity, moisture
resistance, and weatherability. Epoxy adhesives, often used with stone, are affected by
cleanliness of surfaces to be bonded and ambient temperature. Curing time increases
with cold temperatures and decreases with warmer temperatures.
Fabricationand Installation
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With the introduction of new systems of fabrication and installation and recent
developments in the design and detailing of stone cutting, support, and anchorage,
costs are better controlled. Correct design of joints, selection of mortars, and use of
sealants affect the quality and durability of installation. Adequate design and detailing of
the anchorage of each piece of stone are required. The size and thickness of the stone
should be established based on physical properties of the stone, its method of
anchorage, and the loads it must resist. Appropriate safety factors should be developed
based on the variability of the stone properties as well as other considerations such as
imperfect workmanship, method of support and anchorage, and degree of exposure of
the cladding installation. Relieving angles for stone support and anchorage may be
necessary to preclude unacceptable loading of the stone. The stone should be protected
from staining and breakage during shipment, delivery, and installation.
Since stone cladding design and detailing vary with type of stone and installation, the
designer should consult stone suppliers, stone-setting specialty contractors, industry
standards (such as ASTM), and other publications to help select and implement a stone
cladding system.
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CONDITIONS AFFECTING DISINTEGRATION
Quarrying
Disintegration of stone is hastened or retarded by the methods employed in quarrying,
seasoning, finishing, and setting the stone.
The excessive use of explosives in quarrying shatters the cohesion of the particles
composing the stone and causes cracks and flaws that make the stone more permeable
to moisture. Small charges of powder, uniformly distributed over the area to be blasted,
have a lesser weakening effect on the stone. Stone cut out by quarrying machinery is
preferable to that blasted or wedged out, because the stone is not jarred and cracked
by this method and because denser faces are produced which render the stone less
permeable to moisture.
The position of the stone in the quarry also affects its durability. Stone taken from the
exposed faces and the top ledges of the quarry is likely to be less durable than
unexposed stone.
Seasoning
Before a stone is placed in a structure, the interstitial moisture, called quarry water or
sap, must be removed by evaporation. This process is termed seasoning, and should be
effected by exposing the stone to the drying action of the atmosphere for some
months; the stone should be stored under cover for protection against rain. If the stone
is not seasoned, the quarry water will be alternately frozen and thawed during a series
of years, and the stone will be broken up.
Finishing
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The life of a stone is dependent on the style of finish given to its exposed faces. A
smooth or polished surface aids in prolonging the life by facilitating the rapid discharge
of rainwater. The methods employed in dressing the stone also affect its life. Minute
fissures that render the stone more susceptible to atmospheric influences are produced
by impact; hence, stones sawed to the required dimensions are more durable than
those hammered and broken to size.
Setting
The position in which the stone is set in the structure affects its ability to resist
disintegration. When stratified stones are placed on edge, and the mortar joints are not
properly filled, water enters between the layers and in freezing causes the stone to
scale off; therefore, laminated stones should be set with their layers horizontal.
The portions of a structure most liable to early decay are those under cornices, belt
courses, window sills, etc., on which the rainwater slowly falls or drips. As a protection
from this source of decay, the under surface of a projecting stone should have a
narrow groove, called a drip, extending its whole length. The water that collects on the
upper surface of the projection flows over the upper edge and down the face to the
under side, where its further progress is interrupted by the drip; it then falls to the
ground.
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CONCLUSION
Stones are versatile material. In order to be able to decide what kind of stone to used
under given conditions, knowledge of the different kinds employed in the various types
of construction is essential. It is not necessary to determine the exact composition of a
stone to be used in a structure, but knowledge should be sufficient to help in selecting
or specifying the stone best adapted to the type of structure.
The properties of a stone that determine its fitness for construction purposes are
durability, strength, hardness, density, and appearance. The quality of a stone is
ascertained approximately from a study of its origin and chemical composition and from
the results of tests and experiments.
Inferences
Stones are used as versatile material irrespective of the properties of it, still its use
remain as same, varying the techniques of implementation and limitations.
SELECTION OF BUILDING STONES
For selection of the stone should be done on the basis of:
Importance of Preliminary Investigation.-
When an important masonry structure is to be built, it is essential to select a stone
that is strong and durable. Probably nothing in engineering construction is so neglected
as the preliminary inspection of building stone.
If it is necessary to employ great quantities of building stone at points where, the
stability of the structure depends on the strength of the stone, an inspection of the
quarry from which the stone is to be obtained should be made. The engineer should
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also inspect some building or structure which contains the same material and has been
standing for a long time. It is well, however, not to depend wholly on inspection either
at the quarry or at a building, but to subject the stone also to laboratory investigation.
References –
1. Whitney, WilliamDwight, and Benjamin E. Smith. The Century dictionary and
cyclopedia, vol 6. New York: Century Co., 1901. 5,221. Print.
2. C.M.Harris,Dictionary of Architecture & Construction
3. World Floor Covering Association
4. Ribenboim, p.180 says that "Despite the nil practical value of the formulas ... [they] may
have some relevance to logicians who wish to understand clearly how various parts of
arithmetic may be deduced from different axiomatzations ... "
5. Hardy & Wright, pp.344—345 "Any one of these formulas (or any similar one) would
attain a different status if the exact value of the number α ... could be expressed
independently of the primes. There seems no likelihood of this, but it cannot be ruled
out as entirely impossible."
6. Ramanujan, Question 723, Papers p. 332
7. Hardy & Wright, p. 337
